Figure 1.
Schematic diagram of the process described in System (1).
Table 1.
Summary of variables and parameters used throughout the paper.
Figure 2.
Relative positions of growth rates for aerobic and glycolytic cell clones.
Growth rates for aerobic (, solid blue line) and glycolytic (
, dashed lines) cell clones are compared for different initial states of the microenvironment (amount of resource
and amount of oxygen
and different relative intrinsic growth rates
and
. One can see that different clone types have higher fitness relative to each other depending on carbon (
) and oxygen (
) availability and the values of intrinsic parameters
and
.
Table 2.
Sample parameter values.
Figure 3.
Quantifying the effects of differences in growth rates of aerobic and glycolytic cell clones.
(a) Changes in the mean number of glycolytic cells over time for
,
(b)
at
for
varied from 5 to 600, evaluated for
(c) Changes in
over time with respect to differences in
for
(d) Changes in
over time with respect to differences in
for
.
Figure 4.
Quantifying the effects of oxygen availability on the growth of aerobic and glycolytic cell clones.
(a) Changes in the mean number of glycolytic cells over time for
(b)
at
for
varied from 5 to 600, evaluated for
(c) Changes in
over time with respect to differences in
for
(d) Changes in
over time with respect to differences in
for
.
Figure 5.
Quantifying the effects of natural death rates on the changes in proportion of glycolytic cell clones in the population.
(a) Changes in the mean number of glycolytic cells over time for (b)
at
for
varied from 5 to 600, evaluated for
(c) Changes in
over time with respect to differences in
for
(d) Changes in
over time with respect to differences in
for
.
Figure 6.
Quantifying the effects of differences in resource uptake rates on the changes in proportion of glycolytic cell clones in the population.
(a) Changes in the mean number of glycolytic cells over time for
,
(note the scale on y-axis) (b)
at
for
varied from 5 to 600, evaluated for
(note the scale on y-axis) (c) Changes in
over time with respect to differences in
for
,
(d) Changes in
over time with respect to differences in
for
.
Figure 7.
Evolutionary suicide can occur when the proportion of glycolytic cells within the total cell population reaches approximately 10% under given parameter values.
Trajectories depict (a) the changes in the mean value of glycolytic cells in the population (b) extracellular carbon
, (c) intracellular carbon
, (d) total population size
over time and (e) the distribution of cell clones
changing over time.
Figure 8.
Changes in the microenvironment can lead to changes in population composition, which in turn can lead to the population evolving away from the dominant aerobic-aerobic “defecting” strategy, which keeps the system stable, to glycolytic-glycolytic “cooperation”, which can eventually lead to evolutionary suicide (cancer killing the patient and thus killing itself).